Skip to main content
Log in

Lattices of right divisors of linear ordinary differential operators

  • Published:
Programming and Computer Software Aims and scope Submit manuscript

Abstract

A lattice of right divisors of a linear ordinary differential operator P is distributive if and only if all factors of the operator P are not parameterized.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. van Hoeij, M., Factorization of Differential Operators with Rational Coefficients, Symbolic Computation, 1997, vol. 24, pp. 537–561.

    MATH  MathSciNet  Google Scholar 

  2. Loewy, A., Über Reduzible Lineara Homogene Differentialgleichungen, Math. Annalen, 1903, vol. 56, pp. 549–584.

    Article  MATH  MathSciNet  Google Scholar 

  3. Loewy, A., Über Vollstanding Reduzible Lineare Homogene Differentialgleichungen, Math. Annalen, 1906, vol. 62, pp. 89–117.

    Article  MATH  MathSciNet  Google Scholar 

  4. Ore, O., Formale Theorie der Linearen Differentialgleichungen (Erster Teil), J. für die Reine und Angewandte Mathematik, 1932, vol. 167, pp. 221–234.

    MATH  Google Scholar 

  5. Ore, O., Formale Theorie der Linearen Differentialgleichungen (Zweiter Teil), J. für die Reine und Angewandte Mathematik, 1932, vol. 168, pp. 233–252.

    MATH  Google Scholar 

  6. Ore, O., Theory of Non-commutative Polynomals, Annals Mathematics, 1933, vol. 34, pp. 480–508.

    MATH  MathSciNet  Google Scholar 

  7. Tsarev, S.P., An Algorithm for Complete Enumeration of All Factorizations of a Linear Ordinary Differential Operator, Proc. of ISSAC’96, ACM, 1996, pp. 226–231.

  8. Tsarev, S.P., Factorization of Linear Partial Differential Operators and Darboux Integrability of Nonlinear PDEs, SIGSAM Bulletin, 1998, vol. 32, no. 4, pp. 21–28. Also Computer Science, E-print cs/9811002. INTERNET URL: http://xxx.lanal.gov/abs/cs.SC/9811002.

    MATH  Google Scholar 

  9. Abramov, S.A. and Tsarcv, S.P., On Peripheral Factorization of Linear Differential Operators, Programmirovanie, 1997, no. 1, pp. 59–67.

  10. Grätzer, G., General Lattice Theory, Berlin: Springer, 1978. Translated under the title Obshchaya teoriya reshetok, Moscow: Mir, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © A.V. Purgin, 2006, published in Programmirovanie, 2006, Vol. 32, No. 2.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Purgin, A.V. Lattices of right divisors of linear ordinary differential operators. Program Comput Soft 32, 90–95 (2006). https://doi.org/10.1134/S036176880602006X

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S036176880602006X

Keywords

Navigation